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February 25th, 2017, 10:48 PM   #1
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Binomial Distribution

Hi everyone. Second question for today. And this question doesn't have answer on my practice book. So I need help from members at this forum.

Q. Between 1872 and 2000, stock prices rose in 74% of the years. Based on this information, and assuming a binomial distribution, what do you think is the probability that the stock market will rise

a) next year?
b) the year after next?
c) For this situation, what assumptions of the binomial distribution might not be
valid?
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February 25th, 2017, 11:05 PM   #2
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show some workings and we'll explore where you're having problems.
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February 25th, 2017, 11:52 PM   #3
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show some workings and we'll explore where you're having problems.
Actually I don't have any ideas how to solved it. Since the distribution covers from 1872 until 2000 how can we use the distribution to estimates the next year probabilities. It seems out from the domain. Or I missing somethings about Binomial approaches?
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February 26th, 2017, 06:14 AM   #4
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Actually I don't have any ideas how to solved it. Since the distribution covers from 1872 until 2000 how can we use the distribution to estimates the next year probabilities. It seems out from the domain. Or I missing somethings about Binomial approaches?
You are missing the really important idea of using experimental or historical evidence on relative frequencies to estimate future probabilities.

If the stock market rose during 95 years out of a total of 128 years, meaning approximately 74% of the time, do you really think that there is a 50% chance it will fall next year. The historical evidence says that a good estimate of the probability of the stock market rising in a future year is 74%.

Of course you are correct that there is no guarantee that the future will be like the past. Perhaps water will flow uphill next year, but past experience says that it will flow downhill so that is how the water company lays its pipes.

And we may be able to analyze the experimental or historical data to refine our estimate so that we can make predictions better than those based on just relative frequency. But the main practical reason that statistics and probability are studied is to let us make predictions that are based on evidence.
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